15.8.12 problem 12

Internal problem ID [3015]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:08:42 AM
CAS classification : [_separable]

\begin{align*} y-x y^{\prime }&=2 y^{2}+2 y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(y(x)-x*diff(y(x),x)=2*(y(x)^2+diff(y(x),x)),y(x), singsol=all)
 

\[ y = \frac {x +2}{2 x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.449 (sec). Leaf size: 32

DSolve[y[x]-x*D[y[x],x]==2*(y[x]^2+D[y[x],x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x+2}{2 x+4+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to \frac {1}{2} \\ \end{align*}